Decorrelation-Based Feature Discovery: Parkinsons-Whole

1 Effect of UPSTM-Based Decorrelation on Feature Discovery

1.0.1 Loading the libraries

library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)

op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)

1.1 Material and Methods

Data from the speech features

1.2 The Data

pd_speech_features <- as.data.frame(read_excel("~/GitHub/FCA/Data/pd_speech_features.xlsx",sheet = "pd_speech_features", range = "A2:ACB758"))

1.2.1 The Average of the Three Repetitions

Each subject had three repeated observations. Here I’ll use the average of the three experiments per subject.

rep1Parkison <- subset(pd_speech_features,RID==1)
rownames(rep1Parkison) <- rep1Parkison$id
rep1Parkison$id <- NULL
rep1Parkison$RID <- NULL
rep1Parkison[,1:ncol(rep1Parkison)] <- sapply(rep1Parkison,as.numeric)

rep2Parkison <- subset(pd_speech_features,RID==2)
rownames(rep2Parkison) <- rep2Parkison$id
rep2Parkison$id <- NULL
rep2Parkison$RID <- NULL
rep2Parkison[,1:ncol(rep2Parkison)] <- sapply(rep2Parkison,as.numeric)

rep3Parkison <- subset(pd_speech_features,RID==3)
rownames(rep3Parkison) <- rep3Parkison$id
rep3Parkison$id <- NULL
rep3Parkison$RID <- NULL
rep3Parkison[,1:ncol(rep3Parkison)] <- sapply(rep3Parkison,as.numeric)

whof <- !(colnames(rep1Parkison) %in% c("gender","class"));
avgParkison <- rep1Parkison;
avgParkison[,whof] <- (rep1Parkison[,whof] + rep2Parkison[,whof] + rep3Parkison[,whof])/3


signedlog <- function(x) { return (sign(x)*log(abs(1.0e12*x)+1.0))}
whof <- !(colnames(avgParkison) %in% c("gender","class"));
avgParkison[,whof] <- signedlog(avgParkison[,whof])

1.2.1.1 Standarize the names for the reporting

studyName <- "Parkinsons"
dataframe <- avgParkison
outcome <- "class"

TopVariables <- 10

thro <- 0.80
cexheat = 0.15

1.3 Generaring the report

1.3.1 Libraries

Some libraries

library(psych)
library(whitening)
library("vioplot")
library("rpart")

1.3.2 Data specs

pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))

rows	col
252	753

pander::pander(table(dataframe[,outcome]))

0	1
64	188

varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]

largeSet <- length(varlist) > 1500 

1.3.3 Scaling the data

Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns

  ### Some global cleaning
  sdiszero <- apply(dataframe,2,sd) > 1.0e-16
  dataframe <- dataframe[,sdiszero]

  varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
  tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
  dataframe <- dataframe[,tokeep]

  varlist <- colnames(dataframe)
  varlist <- varlist[varlist != outcome]
  
  iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples



dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData

1.4 The heatmap of the data

numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000


if (!largeSet)
{

  hm <- heatMaps(data=dataframeScaled[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 xlab="Feature",
                 ylab="Sample",
                 srtCol=45,
                 srtRow=45,
                 cexCol=cexheat,
                 cexRow=cexheat
                 )
  par(op)
}

1.4.0.1 Correlation Matrix of the Data

The heat map of the data

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  #cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
  cormat <- cor(dataframe[,varlist],method="pearson")
  cormat[is.na(cormat)] <- 0
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Original Correlation",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.9999951

1.5 The decorrelation

DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#> 
#>  tqwt_maxValue_dec_8 det_LT_TKEO_mean_1_coef tqwt_skewnessValue_dec_1 tqwt_skewnessValue_dec_34 mean_delta_delta_0th tqwt_skewnessValue_dec_9 
#>              PPE              DFA             RPDE        numPulses 
#>        0.3198925        0.2836022        0.3037634        0.8534946 
#> numPeriodsPulses meanPeriodPulses 
#>        0.8494624        0.3830645 
#> 
#>  Included: 744 , Uni p: 0.0002016129 , Base Size: 80 , Rcrit: 0.2212033 
#> 
#> 
 1 <R=1.000,thr=0.950>, Top: 74< 47 >[Fa= 74 ]( 74 , 256 , 0 ),<|><>Tot Used: 330 , Added: 256 , Zero Std: 0 , Max Cor: 1.000
#> 
 2 <R=1.000,thr=0.950>, Top: 36< 8 >[Fa= 109 ]( 36 , 95 , 74 ),<|><>Tot Used: 391 , Added: 95 , Zero Std: 0 , Max Cor: 0.999
#> 
 3 <R=0.999,thr=0.950>, Top: 19< 5 >[Fa= 127 ]( 18 , 42 , 109 ),<|><>Tot Used: 421 , Added: 42 , Zero Std: 0 , Max Cor: 0.999
#> 
 4 <R=0.999,thr=0.950>, Top: 3< 2 >[Fa= 130 ]( 3 , 6 , 127 ),<|><>Tot Used: 424 , Added: 6 , Zero Std: 0 , Max Cor: 0.950
#> 
 5 <R=0.950,thr=0.900>, Top: 74< 2 >[Fa= 162 ]( 71 , 92 , 130 ),<|><>Tot Used: 460 , Added: 92 , Zero Std: 0 , Max Cor: 0.981
#> 
 6 <R=0.981,thr=0.950>, Top: 2< 1 >[Fa= 162 ]( 2 , 2 , 162 ),<|><>Tot Used: 460 , Added: 2 , Zero Std: 0 , Max Cor: 0.949
#> 
 7 <R=0.949,thr=0.900>, Top: 12< 1 >[Fa= 165 ]( 11 , 13 , 162 ),<|><>Tot Used: 461 , Added: 13 , Zero Std: 0 , Max Cor: 0.978
#> 
 8 <R=0.978,thr=0.950>, Top: 1< 1 >[Fa= 165 ]( 1 , 1 , 165 ),<|><>Tot Used: 461 , Added: 1 , Zero Std: 0 , Max Cor: 0.912
#> 
 9 <R=0.912,thr=0.900>, Top: 2< 1 >[Fa= 165 ]( 2 , 2 , 165 ),<|><>Tot Used: 461 , Added: 2 , Zero Std: 0 , Max Cor: 0.900
#> 
 10 <R=0.900,thr=0.800>, Top: 76< 5 >[Fa= 191 ]( 70 , 119 , 165 ),<|><>Tot Used: 497 , Added: 119 , Zero Std: 0 , Max Cor: 0.956
#> 
 11 <R=0.956,thr=0.950>, Top: 1< 1 >[Fa= 191 ]( 1 , 1 , 191 ),<|><>Tot Used: 497 , Added: 1 , Zero Std: 0 , Max Cor: 0.948
#> 
 12 <R=0.948,thr=0.900>, Top: 4< 1 >[Fa= 193 ]( 4 , 4 , 191 ),<|><>Tot Used: 497 , Added: 4 , Zero Std: 0 , Max Cor: 0.900
#> 
 13 <R=0.900,thr=0.800>, Top: 23< 1 >[Fa= 198 ]( 21 , 27 , 193 ),<|><>Tot Used: 504 , Added: 27 , Zero Std: 0 , Max Cor: 0.921
#> 
 14 <R=0.921,thr=0.900>, Top: 1< 1 >[Fa= 199 ]( 1 , 1 , 198 ),<|><>Tot Used: 504 , Added: 1 , Zero Std: 0 , Max Cor: 0.900
#> 
 15 <R=0.900,thr=0.800>, Top: 7< 2 >[Fa= 200 ]( 7 , 8 , 199 ),<|><>Tot Used: 506 , Added: 8 , Zero Std: 0 , Max Cor: 0.834
#> 
 16 <R=0.834,thr=0.800>, Top: 2< 1 >[Fa= 200 ]( 2 , 2 , 200 ),<|><>Tot Used: 506 , Added: 2 , Zero Std: 0 , Max Cor: 0.799
#> 
 17 <R=0.799,thr=0.800>
#> 
 [ 17 ], 0.798067 Decor Dimension: 506 Nused: 506 . Cor to Base: 267 , ABase: 744 , Outcome Base: 0 
#> 
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]

pander::pander(sum(apply(dataframe[,varlist],2,var)))

57178

pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))

55135

pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))

4.68

pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))

3.21

varratio <- attr(DEdataframe,"VarRatio")

pander::pander(tail(varratio))

La_app_entropy_shannon_5_coef	La_app_det_TKEO_mean_6_coef	La_app_LT_TKEO_mean_10_coef	La_app_det_TKEO_mean_8_coef	La_app_entropy_log_8_coef	La_app_LT_TKEO_mean_9_coef
5.19e-05	3.63e-05	2.71e-05	1.08e-05	3.25e-06	2.64e-06

1.5.1 The decorrelation matrix

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  
  UPLTM <- attr(DEdataframe,"UPLTM")
  
  gplots::heatmap.2(1.0*(abs(UPLTM)>0),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Decorrelation matrix",
                    cexRow = cexheat,
                    cexCol = cexheat,
                   srtCol=45,
                   srtRow=45,
                    key.title=NA,
                    key.xlab="|Beta|>0",
                    xlab="Output Feature", ylab="Input Feature")
  
  par(op)
  
  
  
}

1.5.2 Formulas Network

Displaying the features associations

par(op)
clustable <- c("To many variables")


  transform <- attr(DEdataframe,"UPLTM") != 0
  tnames <- colnames(transform)
  colnames(transform) <- str_remove_all(colnames(transform),"La_")
  transform <- abs(transform*cor(dataframe[,rownames(transform)])) # The weights are proportional to the observed correlation
  
  
  fscore <- attr(DEdataframe,"fscore")
  VertexSize <- fscore # The size depends on the variable independence relevance (fscore)
  names(VertexSize) <- str_remove_all(names(VertexSize),"La_")
  VertexSize <- 10*(VertexSize-min(VertexSize))/(max(VertexSize)-min(VertexSize)) # Normalization

  VertexSize <- VertexSize[rownames(transform)]
  rsum <- apply(1*(transform !=0),1,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
  csum <- apply(1*(transform !=0),2,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
  
  ntop <- min(10,length(rsum))


  topfeatures <- unique(c(names(rsum[order(-rsum)])[1:ntop],names(csum[order(-csum)])[1:ntop]))
  rtrans <- transform[topfeatures,]
  csum <- (apply(1*(rtrans !=0),2,sum) > 1*(colnames(rtrans) %in% topfeatures))
  rtrans <- rtrans[,csum]
  topfeatures <- unique(c(topfeatures,colnames(rtrans)))
  print(ncol(transform))

[1] 506

  transform <- transform[topfeatures,topfeatures]
  print(ncol(transform))

[1] 221

  if (ncol(transform)>100)
  {
    csum <- apply(1*(transform !=0),1,sum) 
    csum <- csum[csum > 1]
    csum <- csum + 0.01*VertexSize[names(csum)]
    csum <- csum[order(-csum)]
    tpsum <- min(20,length(csum))
    trsum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
    rtrans <- transform[trsum,]
    topfeatures <- unique(c(rownames(rtrans),colnames(rtrans)))
    transform <- transform[topfeatures,topfeatures]
    if (nrow(transform) > 150)
    {
      csum <- apply(1*(rtrans != 0 ),2,sum)
      csum <- csum + 0.01*VertexSize[names(csum)]
      csum <- csum[order(-csum)]
      tpsum <- min(130,length(csum))
      csum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
      csum <- unique(c(trsum,csum))
      transform <- transform[csum,csum]
    }
    print(ncol(transform))
  }

[1] 130

    if (ncol(transform) < 150)
    {

      gplots::heatmap.2(transform,
                        trace = "none",
                        mar = c(5,5),
                        col=rev(heat.colors(5)),
                        main = "Red Decorrelation matrix",
                        cexRow = cexheat,
                        cexCol = cexheat,
                       srtCol=45,
                       srtRow=45,
                        key.title=NA,
                        key.xlab="|Beta|>0",
                        xlab="Output Feature", ylab="Input Feature")
  
      par(op)
      VertexSize <- VertexSize[colnames(transform)]
      gr <- graph_from_adjacency_matrix(transform,mode = "directed",diag = FALSE,weighted=TRUE)
      gr$layout <- layout_with_fr
      
      fc <- cluster_optimal(gr)
      plot(fc, gr,
           edge.width = 2*E(gr)$weight,
           vertex.size=VertexSize,
           edge.arrow.size=0.5,
           edge.arrow.width=0.5,
           vertex.label.cex=(0.15+0.05*VertexSize),
           vertex.label.dist=0.5 + 0.05*VertexSize,
           main="Top Feature Association")
      
      varratios <- varratio
      fscores <- fscore
      names(varratios) <- str_remove_all(names(varratios),"La_")
      names(fscores) <- str_remove_all(names(fscores),"La_")

      dc <- getLatentCoefficients(DEdataframe)
      theCharformulas <- attr(dc,"LatentCharFormulas")

      
      clustable <- as.data.frame(cbind(Variable=fc$names,
                                       Formula=as.character(theCharformulas[paste("La_",fc$names,sep="")]),
                                       Class=fc$membership,
                                       ResidualVariance=round(varratios[fc$names],3),
                                       Fscore=round(fscores[fc$names],3)
                                       )
                                 )
      rownames(clustable) <- str_replace_all(rownames(clustable),"__","_")
      clustable$Variable <- NULL
      clustable$Class <- as.integer(clustable$Class)
      clustable$ResidualVariance <- as.numeric(clustable$ResidualVariance)
      clustable$Fscore <- as.numeric(clustable$Fscore)
      clustable <- clustable[order(-clustable$Fscore),]
      clustable <- clustable[order(clustable$Class),]
      clustable <- clustable[clustable$Fscore >= -1,]
      topv <- min(50,nrow(clustable))
      clustable <- clustable[1:topv,]
    }

pander::pander(clustable)

	Formula	Class	ResidualVariance	Fscore
app_LT_TKEO_mean_8_coef	NA	1	1.000	60
app_det_TKEO_mean_9_coef	+ app_det_TKEO_mean_9_coef - (5.010)app_LT_TKEO_mean_8_coef	1	0.021	12
app_LT_TKEO_std_10_coef	- (0.998)app_LT_TKEO_mean_8_coef + app_LT_TKEO_std_10_coef	1	0.000	9
app_det_TKEO_mean_3_coef	+ app_det_TKEO_mean_3_coef - (2.259)app_det_TKEO_mean_9_coef + (6.541)app_LT_TKEO_mean_8_coef	1	0.031	6
app_entropy_shannon_2_coef	+ app_entropy_shannon_2_coef + (5.456)app_LT_TKEO_mean_8_coef	1	0.029	2
app_entropy_shannon_6_coef	+ app_entropy_shannon_6_coef + (5.392)app_LT_TKEO_mean_8_coef	1	0.019	2
numPulses	+ numPulses - (2.494)app_LT_TKEO_mean_8_coef	1	0.237	1
app_entropy_shannon_7_coef	- (1.009)app_entropy_shannon_6_coef + app_entropy_shannon_7_coef - (0.062)app_LT_TKEO_mean_8_coef	1	0.000	1
app_det_TKEO_mean_5_coef	+ app_det_TKEO_mean_5_coef - (2.028)app_det_TKEO_mean_7_coef + (0.995)app_det_TKEO_mean_9_coef + (0.167)app_LT_TKEO_mean_8_coef	1	0.001	1
VFER_entropy	+ VFER_entropy - (8.817)app_LT_TKEO_mean_8_coef	1	0.297	0
app_entropy_shannon_1_coef	+ app_entropy_shannon_1_coef - (1.112)app_entropy_shannon_2_coef - (0.588)app_LT_TKEO_mean_8_coef	1	0.000	0
app_det_TKEO_mean_7_coef	+ app_det_TKEO_mean_7_coef - (1.109)app_det_TKEO_mean_9_coef + (0.552)app_LT_TKEO_mean_8_coef	1	0.001	0
app_LT_TKEO_mean_10_coef	- (0.224)app_LT_TKEO_mean_8_coef + app_LT_TKEO_mean_10_coef - (0.777)app_LT_TKEO_std_10_coef	1	0.000	0
app_LT_TKEO_std_3_coef	- (0.976)app_LT_TKEO_mean_8_coef + app_LT_TKEO_std_3_coef	1	0.061	0
app_LT_TKEO_std_6_coef	- (0.997)app_LT_TKEO_mean_8_coef + app_LT_TKEO_std_6_coef	1	0.007	0
app_LT_entropy_shannon_8_coef	+ (0.913)app_entropy_shannon_6_coef - (0.905)app_entropy_shannon_7_coef + app_LT_entropy_shannon_8_coef - (4.350)app_LT_TKEO_mean_8_coef + (5.527)app_LT_TKEO_std_10_coef	1	0.001	-1
Ea	+ Ea + (0.029)app_det_TKEO_mean_9_coef - (0.145)app_LT_TKEO_mean_8_coef	1	0.225	-1
app_entropy_log_10_coef	+ app_entropy_log_10_coef + (1.062)app_LT_TKEO_mean_8_coef - (1.361)app_LT_TKEO_std_10_coef	1	0.003	-1
app_det_TKEO_mean_10_coef	- (0.915)app_det_TKEO_mean_9_coef + app_det_TKEO_mean_10_coef - (0.438)app_LT_TKEO_mean_8_coef	1	0.000	-1
Ea2	+ Ea2 + (0.036)app_LT_TKEO_mean_8_coef - (0.162)app_LT_TKEO_mean_10_coef + (0.126)app_LT_TKEO_std_10_coef	1	0.286	-1
det_LT_TKEO_mean_1_coef	NA	2	1.000	22
det_LT_TKEO_mean_4_coef	- (0.560)det_LT_TKEO_mean_1_coef + det_LT_TKEO_mean_4_coef	2	0.136	5
det_TKEO_mean_1_coef	+ det_TKEO_mean_1_coef - (0.961)det_LT_TKEO_mean_1_coef - (4.648)app_LT_TKEO_mean_8_coef	2	0.006	3
det_LT_TKEO_mean_3_coef	- (0.655)det_LT_TKEO_mean_1_coef + det_LT_TKEO_mean_3_coef	2	0.077	2
Ed2_2_coef	+ Ed2_2_coef - (0.791)det_LT_TKEO_mean_1_coef	2	0.028	1
det_TKEO_mean_2_coef	+ det_TKEO_mean_2_coef - (0.774)det_LT_TKEO_mean_1_coef	2	0.042	0
det_TKEO_mean_3_coef	+ det_TKEO_mean_3_coef - (0.617)det_LT_TKEO_mean_1_coef	2	0.082	0
Ed2_1_coef	+ Ed2_1_coef - (0.980)det_LT_TKEO_mean_1_coef	2	0.002	0
det_TKEO_std_5_coef	- (1.039)det_TKEO_mean_1_coef + det_TKEO_std_5_coef - (0.920)Ed2_5_coef + (0.998)det_LT_TKEO_mean_1_coef	2	0.011	-1
tqwt_stdValue_dec_35	NA	3	1.000	21
tqwt_stdValue_dec_33	+ tqwt_stdValue_dec_33 - (0.783)tqwt_stdValue_dec_35	3	0.162	8
tqwt_stdValue_dec_34	+ tqwt_stdValue_dec_34 - (0.936)tqwt_stdValue_dec_35	3	0.016	5
tqwt_stdValue_dec_32	+ tqwt_stdValue_dec_32 - (0.963)tqwt_stdValue_dec_33	3	0.051	4
tqwt_stdValue_dec_31	+ tqwt_stdValue_dec_31 - (1.872)tqwt_stdValue_dec_32 + (1.803)tqwt_stdValue_dec_33 - (1.690)tqwt_stdValue_dec_34 + (0.905)tqwt_stdValue_dec_35	3	0.034	1
tqwt_minValue_dec_30	+ (0.571)tqwt_stdValue_dec_35 + tqwt_minValue_dec_30	3	0.315	1
tqwt_energy_dec_35	+ tqwt_energy_dec_35 - (1.190)tqwt_stdValue_dec_35	3	0.347	0
tqwt_entropy_shannon_dec_35	+ tqwt_entropy_shannon_dec_35 - (1.730)tqwt_stdValue_dec_35	3	0.005	0
tqwt_entropy_log_dec_35	+ tqwt_entropy_log_dec_35 - (0.213)tqwt_stdValue_dec_35	3	0.128	0
tqwt_TKEO_std_dec_35	+ tqwt_TKEO_std_dec_35 - (1.820)tqwt_stdValue_dec_35	3	0.039	0
tqwt_stdValue_dec_36	- (1.124)tqwt_stdValue_dec_35 + tqwt_stdValue_dec_36	3	0.049	0
tqwt_minValue_dec_33	+ (0.897)tqwt_stdValue_dec_33 + tqwt_minValue_dec_33	3	0.090	0
tqwt_minValue_dec_35	+ (0.892)tqwt_stdValue_dec_35 + tqwt_minValue_dec_35	3	0.053	0
tqwt_maxValue_dec_8	NA	4	1.000	18
tqwt_minValue_dec_3	+ tqwt_minValue_dec_3 + (0.806)tqwt_maxValue_dec_8	4	0.312	7
tqwt_minValue_dec_12	+ tqwt_minValue_dec_12 + (0.880)tqwt_maxValue_dec_8	4	0.236	7
tqwt_stdValue_dec_7	+ tqwt_stdValue_dec_7 - (1.185)tqwt_maxValue_dec_8	4	0.156	6
tqwt_stdValue_dec_9	+ tqwt_stdValue_dec_9 - (1.051)tqwt_maxValue_dec_8	4	0.167	6
tqwt_entropy_shannon_dec_6	+ tqwt_entropy_shannon_dec_6 - (2.278)tqwt_maxValue_dec_8	4	0.278	5
tqwt_entropy_shannon_dec_11	+ tqwt_entropy_shannon_dec_11 - (1.652)tqwt_maxValue_dec_8	4	0.340	2
tqwt_entropy_log_dec_8	+ tqwt_entropy_log_dec_8 - (0.170)tqwt_maxValue_dec_8	4	0.282	1

par(op)

1.6 The heatmap of the decorrelated data

if (!largeSet)
{

  hm <- heatMaps(data=DEdataframe[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 cexRow = cexheat,
                 cexCol = cexheat,
                 srtCol=45,
                 srtRow=45,
                 xlab="Feature",
                 ylab="Sample")
  par(op)
}

1.7 The correlation matrix after decorrelation

if (!largeSet)
{

  cormat <- cor(DEdataframe[,varlistc],method="pearson")
  cormat[is.na(cormat)] <- 0
  
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Correlation after ILAA",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  
  par(op)
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.79933

1.8 U-MAP Visualization of features

1.8.1 The UMAP on Raw Data

  classes <- unique(dataframe[1:numsub,outcome])
  raincolors <- rainbow(length(classes))
  names(raincolors) <- classes
  topvars <- univariate_BinEnsemble(dataframe,outcome)
  lso <- LASSO_MIN(formula(paste(outcome,"~.")),dataframe,family="binomial")
  topvars <- unique(c(names(topvars),lso$selectedfeatures))
  pander::pander(head(topvars))

std_9th_delta_delta, tqwt_entropy_log_dec_12, std_delta_log_energy, std_delta_delta_log_energy, tqwt_TKEO_std_dec_12 and std_8th_delta_delta

#  names(topvars)
#if (nrow(dataframe) < 1000)
#{
  datasetframe.umap = umap(scale(dataframe[1:numsub,topvars]),n_components=2)
#  datasetframe.umap = umap(dataframe[1:numsub,varlist],n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
  text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])

#}

1.8.2 The decorralted UMAP

  varlistcV <- names(varratio[varratio >= 0.01])
  topvars <- univariate_BinEnsemble(DEdataframe[,varlistcV],outcome)
  lso <- LASSO_MIN(formula(paste(outcome,"~.")),DEdataframe[,varlistcV],family="binomial")
  topvars <- unique(c(names(topvars),lso$selectedfeatures))
  pander::pander(head(topvars))

std_delta_log_energy, La_tqwt_kurtosisValue_dec_33, La_tqwt_stdValue_dec_32, std_9th_delta, tqwt_entropy_log_dec_13 and mean_MFCC_2nd_coef

  varlistcV <- varlistcV[varlistcV != outcome]
  
#  DEdataframe[,outcome] <- as.numeric(DEdataframe[,outcome])
#if (nrow(dataframe) < 1000)
#{
  datasetframe.umap = umap(scale(DEdataframe[1:numsub,topvars]),n_components=2)
#  datasetframe.umap = umap(DEdataframe[1:numsub,varlistcV],n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After ILAA",t='n')
  text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])

#}

1.9 Univariate Analysis

1.9.1 Univariate

univarRAW <- uniRankVar(varlist,
               paste(outcome,"~1"),
               outcome,
               dataframe,
               rankingTest="AUC")

100 : std_MFCC_2nd_coef 200 : app_entropy_log_3_coef 300 : app_LT_TKEO_mean_7_coef 400 : tqwt_entropy_log_dec_15 500 : tqwt_medianValue_dec_7
600 : tqwt_stdValue_dec_35 700 : tqwt_skewnessValue_dec_27

univarDe <- uniRankVar(varlistc,
               paste(outcome,"~1"),
               outcome,
               DEdataframe,
               rankingTest="AUC",
               )

100 : La_std_MFCC_2nd_coef 200 : app_entropy_log_3_coef 300 : La_app_LT_TKEO_mean_7_coef 400 : La_tqwt_entropy_log_dec_15 500 : tqwt_medianValue_dec_7
600 : tqwt_stdValue_dec_35 700 : tqwt_skewnessValue_dec_27

1.9.2 Final Table

univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")

##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
std_delta_delta_log_energy	23.4	0.469	22.8	0.461	0.653	0.798
std_delta_log_energy	24.3	0.477	23.8	0.441	0.634	0.794
std_9th_delta_delta	23.6	0.242	23.4	0.171	0.746	0.787
std_8th_delta_delta	23.7	0.240	23.4	0.150	0.725	0.780
std_7th_delta_delta	23.7	0.261	23.5	0.188	0.931	0.776
tqwt_entropy_log_dec_12	-39.6	0.239	-39.4	0.240	0.887	0.770
std_6th_delta_delta	23.8	0.277	23.5	0.172	0.945	0.768
std_8th_delta	24.4	0.245	24.2	0.163	0.981	0.767
std_9th_delta	24.4	0.249	24.1	0.185	0.398	0.764
tqwt_entropy_shannon_dec_12	30.3	1.993	32.1	1.703	0.196	0.763

topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]


pander::pander(finalTable)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
std_delta_log_energy	24.335	0.477	23.810	0.441	6.34e-01	0.794
std_9th_delta	24.365	0.249	24.134	0.185	3.98e-01	0.764
La_tqwt_entropy_log_dec_28	-0.633	0.430	-0.819	0.273	1.25e-07	0.758
tqwt_entropy_log_dec_13	-39.232	0.280	-38.985	0.259	7.85e-01	0.757
mean_MFCC_2nd_coef	21.360	18.112	1.716	27.881	4.61e-07	0.753
La_tqwt_energy_dec_33	1.020	0.115	1.133	0.148	6.93e-01	0.746
La_tqwt_kurtosisValue_dec_33	3.501	0.262	3.258	0.389	2.39e-01	0.746
std_12th_delta	24.239	0.239	24.055	0.193	3.42e-01	0.734
La_apq11Shimmer	2.150	0.161	2.031	0.133	4.19e-01	0.734
La_tqwt_stdValue_dec_32	1.137	0.203	0.926	0.323	3.47e-01	0.733

dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")


pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))

mean	total	fraction
2.65	460	0.617

theCharformulas <- attr(dc,"LatentCharFormulas")

topvar <- rownames(tableRaw)
finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])


orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]
finalTable$varratio <- varratio[rownames(finalTable)]

Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores","varratio")

finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])

	DecorFormula	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC	RAWAUC	fscores	varratio
std_delta_delta_log_energy	NA	23.357	0.469	22.794	0.461	6.53e-01	0.798	0.798	NA	NA
std_delta_log_energy	NA	24.335	0.477	23.810	0.441	6.34e-01	0.794	0.794	2	1.00000
std_9th_delta_delta	NA	23.630	0.242	23.388	0.171	7.46e-01	0.787	0.787	NA	NA
std_8th_delta_delta	NA	23.660	0.240	23.428	0.150	7.25e-01	0.780	0.780	NA	NA
std_7th_delta_delta	NA	23.732	0.261	23.479	0.188	9.31e-01	0.776	0.776	NA	NA
tqwt_entropy_log_dec_12	NA	-39.634	0.239	-39.390	0.240	8.87e-01	0.770	0.770	NA	NA
std_6th_delta_delta	NA	23.800	0.277	23.548	0.172	9.45e-01	0.768	0.768	NA	NA
std_8th_delta	NA	24.406	0.245	24.175	0.163	9.81e-01	0.767	0.767	NA	NA
std_9th_delta	NA	24.365	0.249	24.134	0.185	3.98e-01	0.764	0.764	5	1.00000
tqwt_entropy_shannon_dec_12	NA	30.301	1.993	32.106	1.703	1.96e-01	0.763	0.763	NA	NA
La_tqwt_entropy_log_dec_28	+ tqwt_entropy_log_dec_28 - (0.981)tqwt_entropy_log_dec_29	-0.633	0.430	-0.819	0.273	1.25e-07	0.758	0.654	-1	0.00858
tqwt_entropy_log_dec_13	NA	-39.232	0.280	-38.985	0.259	7.85e-01	0.757	0.757	4	1.00000
mean_MFCC_2nd_coef	NA	21.360	18.112	1.716	27.881	4.61e-07	0.753	0.753	0	1.00000
La_tqwt_energy_dec_33	- (1.014)tqwt_energy_dec_32 + tqwt_energy_dec_33 + (1.770)tqwt_stdValue_dec_32 - (1.705)tqwt_stdValue_dec_33	1.020	0.115	1.133	0.148	6.93e-01	0.746	0.509	-3	0.00454
La_tqwt_kurtosisValue_dec_33	- (0.887)tqwt_kurtosisValue_dec_32 + tqwt_kurtosisValue_dec_33	3.501	0.262	3.258	0.389	2.39e-01	0.746	0.628	-1	0.12500
std_12th_delta	NA	24.239	0.239	24.055	0.193	3.42e-01	0.734	0.734	2	1.00000
La_apq11Shimmer	- (0.907)locShimmer + apq11Shimmer	2.150	0.161	2.031	0.133	4.19e-01	0.734	0.713	-1	0.10276
La_tqwt_stdValue_dec_32	+ tqwt_stdValue_dec_32 - (0.963)tqwt_stdValue_dec_33	1.137	0.203	0.926	0.323	3.47e-01	0.733	0.573	4	0.05089

1.10 Comparing ILAA vs PCA vs EFA

1.10.1 PCA

featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE,tol=0.01)   #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous]) 
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)

#pander::pander(pc$rotation)


PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])


  gplots::heatmap.2(abs(PCACor),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "PCA Correlation",
                    cexRow = 0.5,
                    cexCol = 0.5,
                     srtCol=45,
                     srtRow= -45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")

1.10.2 EFA

EFAdataframe <- dataframeScaled

if (length(iscontinous) < 2000)
{
  topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)-1)
  if (topred < 2) topred <- 2
  
  uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE)  # EFA analysis
  predEFA <- predict(uls,dataframeScaled[,iscontinous])
  EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
  colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous]) 


  
  EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
  
  
    gplots::heatmap.2(abs(EFACor),
                      trace = "none",
    #                  scale = "row",
                      mar = c(5,5),
                      col=rev(heat.colors(5)),
                      main = "EFA Correlation",
                      cexRow = 0.5,
                      cexCol = 0.5,
                       srtCol=45,
                       srtRow= -45,
                      key.title=NA,
                      key.xlab="Pearson Correlation",
                      xlab="Feature", ylab="Feature")
}

1.11 Effect on CAR modeling

par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(rawmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
  }

pander::pander(table(dataframe[,outcome],pr))

	0	1
0	39	25
1	3	185

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.889	0.843	0.925
3	se	0.984	0.954	0.997
4	sp	0.609	0.479	0.729
6	diag.or	96.200	27.662	334.550

par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe[,c(outcome,varlistcV)],control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(IDeAmodel,main="ILAA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(IDeAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
  }

pander::pander(table(DEdataframe[,outcome],pr))

	0	1
0	52	12
1	12	176

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.905	0.862	0.938
3	se	0.936	0.891	0.967
4	sp	0.812	0.695	0.899
6	diag.or	63.556	26.952	149.873

par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
  plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
  text(PCAmodel, use.n = TRUE,cex=0.75)
  ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}

pander::pander(table(PCAdataframe[,outcome],pr))

	0	1
0	40	24
1	14	174

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.849	0.799	0.891
3	se	0.926	0.878	0.959
4	sp	0.625	0.495	0.743
6	diag.or	20.714	9.850	43.561

par(op)

1.11.1 EFA

  EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
  EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
  pr <- predict(EFAmodel,EFAdataframe,type = "class")
  
  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(EFAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
  }

  pander::pander(table(EFAdataframe[,outcome],pr))

	0	1
0	32	32
1	5	183

  pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.853	0.803	0.894
3	se	0.973	0.939	0.991
4	sp	0.500	0.372	0.628
6	diag.or	36.600	13.269	100.950

  par(op)